시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 512 MB 6 4 4 66.667%

문제

You are given a list of n integers a1, . . . , an. You can perform the following operation: choose some ai and multiply it by any positive integer.

Your task is to compute the minimum number of different integers that could be on the list after k operations for all 0 ≤ k ≤ n.

입력

The first line of the input contains single integer n (1 ≤ n ≤ 3·105). The second line of the input contains n integers ai (1 ≤ ai ≤ 106).

출력

Output a single line that contains n + 1 integers. The i-th integer should be the minimum possible number of different integers in the list after i − 1 operations.

예제 입력 1

6
3 4 1 2 1 2

예제 출력 1

4 4 3 3 2 2 1